All Questions
18
questions
3
votes
0
answers
53
views
Existence of eigenstates in the context of continuous energies in the Lippmann-Schwinger equation
In the book QFT by Schwartz, in section 4.1 "Lippmann-Schwinger equation", he says that:
If we write Hamiltonian as $H=H_0+V$ and the energies are continuous, and we have eigenstate of $H_0$...
- 57
2
votes
3
answers
112
views
How do vacuum bubbles "dress" terms in the $S$-matrix numerator?
I am self-studying QFT using the book "A modern introduction to quantum field theory" by Maggiore. On page 124-125 he's doing the calculation in the interaction picture for a process with ...
- 613
2
votes
1
answer
88
views
How is dimensionality of $S$ preserved term by term in a perturbative expansion?
In a schematic notation, the scattering matrix element $$\langle p_{out}|S|p_{in}\rangle := 1 + i (2 \pi)^4 \delta^4(p_{in} -p_{out}) M$$ between an incoming state with momentum $|p_{in}\rangle$ and ...
- 307
4
votes
2
answers
296
views
Derivation of Peskin & Schroeder eq. (4.29)
Background material:
These are the parts that I can follow.
Previously Peskin & Schroeder have derived already the expression of the interaction ground state $|\Omega\rangle$ in terms of the free ...
- 838
1
vote
1
answer
181
views
Calculate first-order term of the $S$-matrix for the $\phi^{4}$ theory [closed]
Before I ask a question, I will start with a small introduction.
I want to evaluate the $S$-matrix order-by-order in an expansion in small $\lambda$ for a $2 \rightarrow 2$ scattering in $\phi^{4}$ ...
- 237
2
votes
2
answers
185
views
Difference of decay amplitude and transition amplitude from initial to final state
In Zwiebachs "A First Course in String Theory" 2nd edition he states in chapter 25.2, that
"the amplitude for an initial state consisting of a $\phi$ particle to turn into a final ...
1
vote
1
answer
158
views
QFT scattering with classical potential
I'm studying chapter 6 section 2 of Peskin and Schroeder, on page 185 the unnumbered equation between 6.29 and 6.30, we are trying to compute the $S$-matrix element of the scattering of an eletron ...
- 789
7
votes
1
answer
292
views
Gell-Mann Low formula vs time independent perturbation
Consider a nonperturbed Hamiltonain $H_0$ and an eigenstate $|\Phi\rangle$ satisfying
$$H_0|\Phi\rangle=E_0|\Phi\rangle.$$
Now consider the perturbed Hamiltonian $H=H_0+\lambda H_1$ and let $H_\...
- 789
0
votes
1
answer
129
views
Should the $S$-matrix always analytic in coupling constant?
If we use Dyson series, the $S$-matrix is always an analytic function of the coupling constant. However, if that is the case, how can non-perturbative effects arise in QFT? My question is, should the $...
- 525
4
votes
1
answer
614
views
Feynman propagator for interacting field
For scalar field, Feynman propagator is commonly defined as
$$
\Delta_F(x-y) = \langle 0 | T\phi(x)\phi(y)|0 \rangle .
$$
For free theory, field satisfy equation of motion is $$\phi(x) = \int\frac{dp^...
- 337
6
votes
1
answer
534
views
What is the role of wave packets in LSZ formulae?
When deriving LSZ formulae, we assume asymptotic particles’ creation/annihilation operators as:
$$a_\text{g,in/out}\ \ (\mathbf{p})\equiv \int d^3k \ g(\mathbf{k}) a_\text{in/out}(\mathbf{k}), \ \text{...
- 1,363
4
votes
1
answer
1k
views
Optical theorem in $\phi^4$: which poles contribute to discontinuity in Feynman amplitude?
Section 7.3 ("The Optical Theorem") in Peskin and Schroeder's QFT text contains a leading order verification of the optical theorem in $\phi^4$ theory by calculating the (discontinuity across the ...
- 545
1
vote
1
answer
456
views
Scattering amplitude calculation using first order Chiral Perturbation Theory Lagrangian
Consider the Chiral Perturbation Lagrangian to first order(quark masses set to zero):
$$L = L^{(2)} = \frac{f^2}{4}tr[\partial_{\mu} U \partial^{\mu} U^{\dagger}] ,$$ where U is a $2 \times 2 $ ...
- 1,574
2
votes
1
answer
736
views
Why this loop carries an integral if there is no undetermined momenta?
Consider the following Feynman diagram:
I've read that it will have associated with it one integral over the loop. The issue is, in Schwartz book the Feynman rules for momentum space are:
Internal ...
- 36.4k
4
votes
2
answers
947
views
Computing S-Matrix Elements from Feynman Diagrams
In Peskin and Schroeder (PS), the Feynman rules for calculating correlation functions are first presented. Only terms involving all field contractions need to be considered.
In Section 4.6, this is ...
- 401